{
  "abstract": "A prolongation variety of a polynomial differential system $S$ is an algebraic variety defined by the equations of $S$ and their derivatives up to a given order. We compute the geometric degree of the prolongation varieties associated with the system $x_1'=x_2^2$, $x_2'=x_1^2$ in terms of the prolongation order, thereby proving a conjecture stated by Gleb Pogudin in Section 2, Question 6 of \"Some Open Problems in Differential Algebra\". Our approach is motivated from the beginning by doing computational experiments in OSCAR in order to find the number of solutions of a zero-dimensional system using algebraic Thomas decomposition. The result will follow from a coprimality condition on a family of polynomials with integer coefficients, which is verified by showing that their roots satisfy a strong interlacing property. Finally, we propose an extension of the conjecture for the systems $x_1'=x_2^n$, $x_2'=x_1^n$ with $n>2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06638",
  "author_total": 1,
  "authors": [
    {
      "name": "Mattia Puddu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4g0xc3mtf75vv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06638",
  "fulltext_url": null,
  "id": "4g0xc3mtf75vv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06638",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06638",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g0xc3mtf75vv.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06638",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06638"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the geometric degree of the prolongation varieties of the differential system $x_1'=x_2^2$, $x_2'=x_1^2$",
  "title_text": "On the geometric degree of the prolongation varieties of the differential system x_1'=x_2^2, x_2'=x_1^2",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/4g0xc3mtf75vv",
  "venue": "arXiv",
  "versions": []
}